Statistics

Problem Statement for "FairTournament"

Problem Statement

Consider a tournament with n participants, numbered 1 to n in decreasing order by strength. The outcome of the tournament is a ranking of all the participants: participant p1 in first place (ranking 1), participant p2 in second place (ranking 2), ..., participant pn in last place (ranking n). It can be easily seen that p is a permutation.

An outcome of the tournament is called k-fair if every participant gets a ranking that differs from his number by at most k. In other words, p is a permutation where the following condition holds for all i: |i-pi|<=k.

Given an int n and an int k, return the number of different possible k-fair outcomes for a n-player tournament. The return value must be a String with no extra leading zeroes.

Definition

Class:
FairTournament
Method:
countPermutations
Parameters:
int, int
Returns:
String
Method signature:
String countPermutations(int n, int k)
(be sure your method is public)

Constraints

  • n will be between 1 and 100, inclusive.
  • k will be between 1 and 6, inclusive.

Examples

  1. 3

    1

    Returns: "3"

    Rankings "1,2,3", "2,1,3" and "1,3,2" are 1-fair, while "2,3,1", "3,1,2" and "3,2,1" are not.

  2. 3

    2

    Returns: "6"

  3. 10

    3

    Returns: "19708"

  4. 100

    1

    Returns: "573147844013817084101"

  5. 1

    1

    Returns: "1"

  6. 5

    2

    Returns: "31"

  7. 9

    3

    Returns: "6404"

  8. 12

    4

    Returns: "1396948"

  9. 14

    5

    Returns: "135025756"

  10. 1

    6

    Returns: "1"

  11. 2

    6

    Returns: "2"

  12. 3

    6

    Returns: "6"

  13. 4

    6

    Returns: "24"

  14. 5

    6

    Returns: "120"

  15. 6

    6

    Returns: "720"

  16. 20

    1

    Returns: "10946"

  17. 33

    2

    Returns: "634245200926"

  18. 42

    3

    Returns: "69850708085388667677"

  19. 57

    4

    Returns: "159128297041016435714751131714066"

  20. 60

    5

    Returns: "198899054347029676663136942820561016192"

  21. 64

    6

    Returns: "704724510370835968978398201517613241969210494"

  22. 77

    1

    Returns: "8944394323791464"

  23. 83

    2

    Returns: "1596437957527888762181476388934"

  24. 78

    3

    Returns: "21837383439504338719488921621840706409"

  25. 93

    4

    Returns: "111494812890123593989212189685194654756253116957177754"

  26. 99

    5

    Returns: "7488476460554583387809300269213525343844718913007616902164197555"

  27. 97

    6

    Returns: "439331534188737229355695791949863554660183606464421634807769978978048"

  28. 100

    6

    Returns: "63966642926037141928677083283801398106777787737963379360032740763763584"

  29. 1

    1

    Returns: "1"

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